The present invention relates generally to a fractal-based method of analyzing topographic data and particularly data which is acquired by the use of electronic profiling, or profilometry, apparatus such as a scanning tunneling microscope (STM), atomic force microscopy (AFM), scanning profilometry, etc. or by stereophotogrametry.
The purpose of the invention is to reduce large topographic data sets and produce parameters that retain the essence of the surface topography for predicting surface behavior and correlating with manufacturing process variables for surface creation.
Interactions with surfaces can be considered to have a characteristic range of sizes or scales over which the interaction takes place. In the case of corrosion or contamination, the characteristic scale would appear to be in the range of atomic sizes, for powder coating it would appear to be the powder size, in the case of machining defects on surfaces on hard aluminum alloys the characteristic size would be the size of the iron rich intermetallic particles in the alloy. To correlate well with behavior or surface creation, the topographic data on which the analysis is based could contain data at the scales characteristic of the interactions; alternatively, fractal analysis could provide means for extrapolating the results of the analysis to finer scales, provided multifractal behavior does not exist in scales over which the extrapolation takes place.
Fractal description of a surface differs from that of which can be provided by Euclidian geometry. Fractal geometry is utilized to describe the random or chaotic nature of the morphologies of surfaces. The area of surfaces, that have a random or chaotic geometric component, is a function of the scale of observation, i.e., the area does not have a unique value but varies with scale.
One method involves sectioning a sample perpendicular to the surface and imaging the resulting profile with scanning electron microscope or optical microscopy. The image is measured so that the profile can be analyzed mathematically. This must be repeated many times to fully characterize a surface. It does not take into account the areas between the profiles and only accounts for the relationship between one profile to adjacent profiles if care is taken in the sectioning.
Stylus profilometry is the most widely used method of gathering topographic data. Profilometry is generally limited to cross sections (i.e., z=z(x)) and consists of approximately 5,000 data points after digitalization. It is possible to scan or raster the surface using a profilometer, although scanning is used infrequently. In conventional stylus profilometry the stylus has a radius of 1 to 10 .mu.m, a finite contact force and is, therefore, insensitive to the fine scales at which many important surface interactions take place. Parameters derived from a box-counting (fractal)analysis of profilometry data have been successfully correlated with cleanability of surfaces contaminated by latex spheres with diameters about ten times smaller than the stylus tip.
STM and AFM produce topographic detail at scales fine enough to include those characteristic of atomic interactions with surfaces. The principle difficulty in dealing with STM and AFM is how to reduce the large sets of topographic points, over 100,000, and retain the qualities of the topography which relate to surface creation and behavior. STM topographic data has been analyzed scan by scan, as if it were profile data. Profile type analyses of STM or AFM data have the advantage of using existing algorithms, although these profile type analyses fail to make use of the information inherently present in the lateral proximity of scans.
Measured surface area of real topographies is a function of the scale of measurement or interaction. There are many topographically dependent phenomena whose intensity depend on the surface area the scale at which they interact with the surface. There is a need for a surface analysis method that can support the systematic and logical design of surfaces, and the processes to create them, a method that can be used to predict the intensity of interactions, e.g., adhesive strength, chemical reactivity, cleanability. This need exists particularly, though not exclusively, on sub-micron scales, where surface topographies of engineering interest tend to have strong random or chaotic components to their geometries, and hence have surface areas that are dependent on the scale of interaction. The topography of the earth's surface has similar properties over certain ranges of scale.
None of the prior art methods determine the relative, or normalized surface areas as a function of an area scale, with a clear physical interpretation. None of the prior art methods use triangles of constant, or substantially similar areas to determine surface areas of topographic data sets as a function of the triangle area. None of the prior art methods deal with design applications.
These and other difficulties experienced with the prior art devices have been obviated in a novel manner by the present Invention.
It is a principal object of the invention to provide a method of providing surface characterizations that are normalized, i.e., don't depend on the actual area which is examined and have clear physical interpretations.
A further object of the invention is to provide a method which is able to distinguish between scale ranges which correspond to smooth and to rough topographies, so that surfaces can be designed that can physically integrate functions which rely on different surface types, without having interferences between the functions.
Another object of the invention is to provide a method of quantifying the topographic structure of a specimen surface from a grid of topographic points by defining the surface in terms of patches which have a predetermined shape and area value to obtain a measured area value and additional measured area values by defining the specimen surface with patches having the same shape and different predetermined area values to provide a plurality of measured area values for analysis of the surface topography of the specimen surface.
A further object of the present invention is the provision of a method of quantifying the topographic structure of a specimen from a grid of topographic data points by defining the surface in terms of patches having a predetermined shape in a manner which enables the data relating to the grid of topographic data points to be stored in the memory of a computer and the surface area calculations in terms of the triangles to be calculated by the computer.
A still further object of the invention is to describe, or characterized, the surface of an object by the way its apparent surface area changes with scale of observation. This description of a surface allows a designer to:
(1) determine the intensity of an interaction (e.g., adhesion, chemical reactivity) with a surface, once the scale of interaction is known by simple multiplication, PA1 (2) determine if it is possible, and if so, how to physically integrate two or more surface related phenomena on one surface while maintaining functional independence, from the scales of interaction of the phenomena, by comparing the scales of interaction to the area of the surface at those scales (or ranges of scales), PA1 (3) design manufacturing processes to create the desired surfaces, for example, by adjusting the scale of interaction of the process with the workpiece material, or by adjusting the constituent size, shape and distribution in a composite workpiece. PA1 (1) keep the area of the triangles constant, PA1 (2) keep the shape of the triangles constant, PA1 (3) completely cover the specimen surface with triangles.
With these and other objects in view, as will be apparent to those skilled in the art, the invention resides in the confirmation of parts set forth in the specification and covered by the claims appended hereto.